The conclusion is that not only do our brains react to poetry and music similarly, but there's even a difference between how we react to poetry versus prose -- and it has to do with our emotional connection we make with the writing itself:

The team [ ... ] found that emotionally charged writing activated areas of the brain which are known to respond to music. Predominantly on the right side, these regions had previously been shown to give rise to the “shivers down the spine” feeling caused by an emotional response to music.
When the team specifically compared poetry to prose, they found evidence that poetry activates brain regions associated with introspection – such as the posterior cingulate cortex and medial temporal lobes.